genus(List) -- Compute the number of gaps (genus) of a semigroup

Synopsis

• Function: genus

• Usage:

  g = genus L

• Inputs:
  • L, a list,
• Outputs:
  • g, an integer,

Description

i1 : genus {4,7}

o1 = 9

i2 : G = gaps {4,7}

o2 = {1, 2, 3, 5, 6, 9, 10, 13, 17}

o2 : List

i3 : #G

o3 = 9

i4 : S = semigroup{4,7}

o4 = {0, 4, 7, 8, 11, 12, 14, 15, 16, 18, 19, 20, 21}

o4 : List

i5 : set G + set S  == set(0..21)

o5 = true

See also

• gaps -- The gap sequence of a semigroup
• semigroup -- Compute the semigroup generated by a list of positive integers